Sunday, November 14, 2010

The Importance of 10 %
Once students understand the importance and significance of 10%, so many other mathematical concepts seem to fall into place.

Before we start a unit on decimals and another on fractions, I like to take a good chunk of time to teach students how to find 10% of a number.  I also like them to understand how and why you are able to convert from fractions to decimals to percents.

We begin this process by building an understanding of what ten percent is.  Ten percent is 1/10th of a number. If you have 20 cookies and you were going to give 10% to your sister, how many cookies are you going to give?

There are a number of ways we can approach this.  I start off by teaching them that you can always just move the decimal point to the left and that is 10%.  So if you do that with this cookie problem, your sister will get 2 cookies.

This still does not help students "get" what 10% is.

So we begin to explore the "10%" itself.  What does the percent sign mean? The students know that it means out of 100 since they have been taking quizzes and tests for a long time.  So 10% means 10 out of 100.  If we simplify that it means 1 out of 10.

Ah, now we are cooking.

Back to the cookie problem.

If students know that 10 percent is 1 out of 10, they can begin to understand that finding percent can be a division process.  Splitting the cookies into 10 equal groups is something students clearly understand whether they like to share or not.   (Once this happens, they understand that 1/8 would lead you to divide by 8,  25% would lead you to divide by 4.)

Taking what you have and breaking it into 10 equal groups makes 10%.  Fortunately, this is a clear, hands-on approach to finding 10 %.  We can take those cookies, split them up equally into 10 groups and find out each person, including your sister will get 2 cookies.  Unfortunately, when you need to do this at a restaurant, you can't do this with a tip, you wont be able to take your money on the table, divide it up into 10 equal groups, find 2 of those groups and then give those groups to your server for a tip.

In class we were able to do this with a large bucket of manipulatives.  Please see a future blog for the estimation of 10 %.

So now students know they can just move the decimal over one place to the left, divide by 10, or split their actual number into 10 equal groups with manipulatives.

The fourth way to find 10% is just to multiply by .1 or .10.  Why does this work?  Because when you multiply by one tenth you are essentially finding 1out of every 10.  The decimal ends up moving over one place to the left after you multiply by .1.

Once students are able to reason and work with 10 %, they are then able to see and find the pattern that follows.

If you can find 10 % of 20 than you can find 20 %.  How?  You just double it.  How would you find 5%?  Cut 10% in half.

Now if you make an organized table, you would have it look something like this:

Percent          of         20

10%                           2
20%                           4

30%                           6

40%                           8

50%                          10

Students are then able to fill in the missing parts.  They can fill in 5%, 15%, 25% all the way up to 100%. Ten percent and 5% put together make 15%.

Percent          of         20
 5%                            1
10%                           2
15%                           3
20%                           4 
25%                           5
30%                           6
35%                           7
40%                           8
45%                           9        
50%                          10

It is a pattern.  Just a pattern once you find the first, most important part...10%
Students can then apply this skill to finding out a 15 or 10% tip at a restaurant.  Than they can figure out how much you spent with the tip in total. They are able to estimate about 10% of an unknown group.

There is much more to this 10% business.  Stay tuned.  In the meantime, please help us find another important strategy that we can use and apply in our class.  Leave a comment to let us know.

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